The BBC and Master Computer Public Domain Library

Normalise FWA#1 [bit-by-bit & byte-by-byte methods supported]

Submitted by Steve Fewell

Routine: anorm[1]
Name: Normalise Floating-Point number in the FWA [bit-by-bit and byte-by-byte methods supported]
Starting Address: &81F7
Entry criteria: The FWA contains a floating-point number.
Exit: FWA has been normalised (The top bit of the FWA is set, and the exponent adjusted accordingly)

Description:
Unlike the Normalise FWA#2 routine, this routine does not have any special entry requirements (i.e. certain bytes of the number needing to be copied to the A and Y registers).

If ?&31 is negative (the FWA Mantissa's top bit is already set) then exit as the number is already normalised.

If FWA's Mantissa byte 1 (?&31) is zero then OR ?&31 with ?&32, ?&33, ?&34 and ?&35. If the result is zero, then the whole Mantissa (and hence, the whole number) is zero, so jump to &81CC to zero the FWA's Exponent, Exponent Overflow and Sign bytes, and exit. 

[Byte-by-Byte method - Normalise one byte at a time]
If FWA's Mantissa byte 1 (?&31) is zero, but the FWA doesn't not contain zero, then Load A with the FWA's Exponent (?&30), and [&8209] move the FWA Mantissa byte 2 to the FWA Mantissa Byte 1, move the FWA Mantissa byte 3 to the FWA Mantissa Byte 2, move the FWA Mantissa byte 4 to the FWA Mantissa Byte 3 and move the FWA Mantissa rounding byte to the FWA Mantissa Byte 4. Set the FWA Mantissa Rounding byte to zero. Subtract 8 from the exponent (as we have moved the number along 8 bits), and decrement the FWA Exponent Overflow (if the Exponent underflowed). If FWA Mantissa Byte 1 is still zero, then we need to normalise by another 8 bits, so jump back to &8209 to move the Mantissa along another byte.
If by moving the Mantissa along byte-by-byte, we now have a normalised number, store A back in the FWA Exponent byte and exit, otherwise jump to &822C to proceed with the bit-by-bit method.

[Bit-by-Bit method - Normalise one bit at a time]
If FWA's Mantissa byte 1 (?&31) is not zero, but the FWA isn't normalised, then Load A with the FWA's Exponent (?&30), and [&822C] subtract 1 from the FWA Exponent byte [A], and decrement the FWA Exponent Overflow byte if the result underflowed, and shift the FWA Mantissa left one bit (multiply by 2) so that the bits move from the ?&35 end of the number to the ?&31 end of it. Keep repeating this until the top bit is set.

Now that the number is normalised, store A back in the FWA Exponent Byte (?&30), and exit.

Disassembly for the Normalise FWA#2 routine